Learning Seminar: the Atiyah-Singer Index Theorem
Learning Seminar: the Atiyah-Singer Index Theorem
Details
4 - 5:30 pm every Thursday in Linde 255.
Contact: nsagman(at)caltech(dot)edu or byyang(at)caltech(dot)edu , Linde 289
We plan to study the Atiyah-Singer Index Theorem and its consequences via heat equation methods. For the time being, the main reference is "Invariance Theory, the Heat Equation, and the Atiyah-Singer Index Theorem" by Peter Gilkey. This is open to discussion and may change later. The first edition can be found for free here. We have a copy of the (much more detailed) second edition in our office. One is welcome to come in and use it at any time.
There are no strict prerequisites for participating, but it would be advantageous to be comfortable with the basics of functional analysis and differential geometry. Despite the fact that characteristic classes are discuss in Ma 151c, we will still cover this because
a) we would like the seminar to be open to first year graduate students
b) Gilkey uses the formalism of Chern-Weil theory, which is only discussed in the appendix of Milnor and Stasheff (text for 151c)
Guidelines for giving a talk
Each talk will be 90 minutes. As for content, one can essentially go over the relevant sections of Gilkey. If you want to use some other source(s) you are certainly welcome to as long as the correct material is covered.
Calendar
References and Further Sources: